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  • chaotic phenomena  (2)
  • Restricted three-body problem  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Celestial mechanics and dynamical astronomy 66 (1996), S. 203-228 
    ISSN: 1572-9478
    Keywords: Restricted three-body problem ; chaotic phenomena ; scattering
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We consider the scattering motion of the planar restricted three-body problem with two equal masses on a circular orbit. Using the methods of chaotic scattering we present results on the structure of scattering functions. Their connection with primitive periodic orbits and the underlying chaotic saddle are studied. Numerical evidence is presented which suggests that in some intervals of the Jacobi integral the system is hyperbolic. The Smale horseshoe found there is built from a countable infinite number of primitive periodic orbits, where the parabolic orbits play a fundamental role.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Celestial mechanics and dynamical astronomy 71 (1998), S. 167-189 
    ISSN: 1572-9478
    Keywords: restricted three‐body problem ; chaotic phenomena ; scattering
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We study the scattering motion of the planar restricted three‐body problem for small mass parameters μ. We consider the symmetric periodic orbits of this system with μ = 0 that collide with the singularity together with the circular and parabolic solutions of the Kepler problem. These divide the parameter space in a natural way and characterize the main features of the scattering problem for small non‐vanishing μ. Indeed, continuation of these orbits yields the primitive periodic orbits of the system for small μ. For different regions of the parameter space, we present scattering functions and discuss the structure of the chaotic saddle. We show that for μ 〈 μc and any Jacobi integral there exist departures from hyperbolicity due to regions of stable motion in phase space. Numerical bounds for μc are given.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
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